For the pivoted QR factorization method [1]}, [2]} applied to the shock-mixing layer flow, we represent the state approximately as a linear combination of the leading three principal components.
Scipy's implementation of pivoted QR factorization found at https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.qr.html was used to select among the 2210 allowable sensors those that allow robust reconstruction of these first three principal components.
We also tried representing the state using more principal components and taking the first three sensor locations chosen via pivoted QR factorization.
As with the case when only three principal components are used, these sensors do not enable nonlinear reconstruction of the state.
